Power Electronics by M H Rashid (1-6 and 9 Chapter), Manuais, Projetos, Pesquisas de Engenharia Elétrica

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BAN Re er eb Remo co ER RE AE Irculation of this edition outside of lhese territories is UNAUTHORIZED Contents Preface xix About the Author xxili Chapter 1 Introduction 1 1.1 Applications of Power Electronics 1 1.1.1 History of Power Electronics 2 12 Power Semiconductor Devices 5 121 PowerDiodes 5 1.2.2 Thyristors 6 123 PowerTransistors 9 Fo CE istics of P Devi 0 1.4 Characteristics and Specifications of Switches 16 Lá Ideal O am 16 2 isties af Practical Devi 1 143 Switch Specifications 18 144 Device Choices 19 1.5 s of Power Electronic Circuits 20 Ló Design of Power Electronics Equipment 23 1.7 Determining the Root-Mean-Square Values of Waveforms 24 1.8 Peripheral Effects 24 L9 PowerModues 26 Li0O Intelligent Modules 26 111 Power Electronics lournals and Conferences 28 Summa: 29 References 29 Review Questi 3 Chapter2 Power Semiconductor Diodes and Circuits 3 2.1 Introduction 3 23 Diode Characteristics 33 vii Copyrighted materia x Contents 6,5 Three-Phasc Inverters 237 6.5.1 180-Degree Conduction 237 6.5.2 120-Degree Conduction 246 6.6 Voltage Control of Single-Phase Inverters 248 6.6.1 Sinple-Pulse-Widih Modulation 248 6.6.2 Multiple-Pulse-Width Modulation 250 664 Si idal Pulse-Width Modulati 253 5 ified Si idal Pulse-Width Modulati 257 6.6.5 | Phase-Displacement Control 258 6.7 Advanced Modulation Techniques 260 6.8 Voltage Control of Three-Phase Inverters 264 6.8.1 Sinusoidal PWM 265 6.82 60-Degree PWM 268 6.8.4 Space Vector Modulation 21 6.8.5 Comparison of PWM Techniques 279 és H ie Reducti 280 9,10 Current-Source Inverters — 285 6.12 BoostInverter 289 6.13 Inverter Circuit Design 294 Summary 299 References 290 Review Questi 300 Problems 30 Chapter 7 Thyristors 304 21 Introduction 304 7.2 Thyristor Characteristics 304 7.3 Two-Transistor Model of Thyristor 307 7.4 Thyristor Tum-On 309 7.5 Thyristor Turn-Off 311 7.6 Thyristor Types 313 : 7.6.1 Phase-Controlled Thyristors 314 La BCTs 34 7.6.3 Fast-Switching Thyristors 315 L64 LASCRs alé 7.6.5 Bidirectional Triode Thyristors 316 Copyrighted material Contents xi Zó.I3 SITHs 328 7.6.14 Comparisons of Thyristors 330 77 Series Operation of Thyristors 330 7.8 Parallel Operation of Thyristors 337 79 did P E EE ZIO doidt Protection 339 7.11 SPICE Thyristor Model 341 7.11.) Thyristor SPICE Model 341 2112 GTOSPICE Model 343 Z113 MCTSPICE Model 345 ZiL4 SITHSPICE Model 345 Summary 346 References ad7 Review Questions 50 Problems — 350 Chapter 8 Resonant Pulse Inverters 352 81 Introduction 352 8.3 Frequency Response of Series-Resonant Inverters 368 83.1 Frequency Response for Series Loaded 368 8.3.2 Frequency Response for Parallel Loaded 370 83.3 Frequency Response for Series-Parallel Loaded 372 84 Parallel Resonant Inverters 374 8.5 Voltage Control of Resonant Inverters 377 86 Class E Resonant Inverter 380 87 ClassE Resonant Rectifier 383 88 Zero-Current-Switching Resonant Converters 388 88.1 L-Type ZCS Resonant Converter 389 8.8.2 M-Ivpe ZCS Resonant Converter 391 8.9 Zero-Voltage-Switching Resonant Converters 393 8.10 Comparisons Between ZCS and ZVS Resonant Converters 396 811 Two-Quadrant ZVS Resonant Converters 396 8.12 Resonant DC-Link Inverters 300 Summary 402 References 403 Review Questions 403 Problems — 404 Chapter 9 Multilevel Inverters 406 91 Introduction 406 9.2 Multilevel Concept 407 Copyrighted material xii Contents 923 es of Multilevel Inverters 408 9.4 Diode-Clamped Multilevel Inverter 409 9.4.1 Principleof Operation 410 9.4.2 Features of Diode-Clamped Inverter 411 9.4.3 Improved Diode-Clamped Inverter 412 9.5 Fiying-Capacitors Multilevel Inverter 414 9.5.1 Principle of Operation 415 9.5.2 Features of Flying-Capacitors Inverter 417 92,6 Cascaded Multilevel Inverter 417 9.61 Principleof Operation 418 2,62 Features of Cascaded Inverter 419 9.7 Applications | 421 9.7.1 Reactive Power Compensation 422 9.7.3 Adjustable Speed Drives 424 9.8 Switching Device Currents 424 9.9 DC-Link Capacitor Voltage Balancing 425 92.10 Features of Multilevel Inverters 427 9.11 Comparisons of Multilevel Converters 428 Summary 428 References 429 Review Questions 430 Problems 430 Chapter 10 Controlled Rectifiers 431 101 Introduction 43] 10.2 Principle of Phase-Controlled Converter Operation 432 10.3 Single-Phase Full Converters 434 10.3.1 | Single-Phase Full Converter with RL Load 438 10,4 Single-Phase Dual Converters 440 10.5 Principle of Three-Phase Half-Wave Converters 443 10.6 Three-Phase Full Converters 447 10.7 Three-Phase Dual Converters 453 10.8 Power Factor Improvements 456 108.1 Extinction Angle Control 456 1082 S etric Angle Control 457 10.83 PWM Control 461 10.84 Single-Phase Sinusoidal PWM 463 10,85 Three-Phasc PWM Rectifier 465 10.9 Single-Phasc Semiconverters 467 10.91 Single-Phase Semiconverter with RL Load 472 10.10 Three-Phase Semiconverters 474 10.10.1 Three-Phase Semiconverters with RL Load 479 10.11 | Single-Phase Series Converters 480 10.12 Twelve-Pulse Converters 485 Chapter 15 Contents xv 14.63 Magnetic Saturation 635 Summary 63% References 636 Review Questions 637 Problems 637 DC Drives 640 15.1 Introduction 640 52 BadeCh jetics Of DC M 641 15.3 Operating Modes 645 15.4 Single-Phase Drives 648 15.5 15.41 Single-Phase Half-Wave-Converter Drives 649 15.4.2 Single-Phase Semiconverter Drives 650 154.3 Single-Phase Full-Converter Drives 651 15.44 Single-Phase Dual-Converter Drives 652 Three-Phase Drives 656 15.51 Three-Phase Half-Wave-Converter Drives 657 15.5.2 Three-Phase Semiconverter Drives 657 15.53 | Three-Phase Full-Converter Drives 657 156 DC-DC Converter Drives 662 15.7 15.6.1 Principleof Power Control 662 15.62 Principle of Regenerative Brake Control 664 15.63 Principle of Rheostatic Brake Control 667 15.6.4 Principle of Combined Regenerative and Rheostatic Brake Control 668 15.6.5 Two- and Four-Quadrant DC-DC Converter Drives 669 15.6.6 Multiphase DC-DC Converters 670 Closed-Loop Control of DC Drives 673 15.71. Open-Loop Transfer Function 673 15.72 Closed-Loop Transfer Function 678 15.73 Phase-Locked-Loop Control 684 15.74 Microcomputer Control of DC Drives 685 Summary 687 References 687 Review Questi 688 Problems 688 Chapter 16 ACDrives 692 16.1 Introduction 692 1 ion Motar Dri 193 16.21 Performance Characteristics 694 16.22 Stator Voltage Control 701 1623 Rotor Voltage Control 703 162.4 Frequency Control q xvi Contents 16.3 16.4 16.5 16.6 16.2.5 Voltage and Frequency Control n3 16.26 Current Control 716 16.27 Voltage, Current, and Frequency Control 720 Closed-Loop Control of Induction Motors 721 Vector Controls 726 16.4.1 Basic Principle of Vector Control 727 16.42 Direct and Quadrature-Axis Transformation 728 L6d3 Indirect Vector Control 734 16.4.4 Director Vector Control 736 Synchronous Motor Drives 738 16.5.1 | Cylindrical Rotor Motors 738 16.52 Salient-Pole Motors 741 16.53 Reluctance Motors 743 16.5.4 | Permanent-Magnet Motors 743 16.5.5 Switched Reluctance Motors 744 16.5.6 Closed-Lovbp Control of Synchronous Motors 745 16.5.7 Brushless DC and AC Motor Drives 747 Stepper Motor Control 749 16.6.1 Variable-Reluctance Stepper Motors 750 16.62 Permanent-Magnet Stepper Motors 753 Summary 756 References 756 Review Questions 757 Problems 758 Chapter 17 | Gate Drive Circuits 761 1a 17.2 17.3 174 17,5 17.6 17.7 17.8 17.9 Introduction 761 MOSFET Gate Drive 761 BJT Base Drive 763 Isolation of Gate and Base Drives 767 17.4.1 Pulse Transformers 769 17.4.2 Optocouplers 769 Thyristor Firing Circuits 770 Unijunction Transistor 772 Programmable Unijunction Transistor 715 Thyristor Converter Gating Circuits Mm Gate Drive [Cs 777 17.91 Drive ICfor Converters 781 17,92 High-Voltage IC for Motor Drives 784 Summary 788 References 789 Review Questions 789 Problems 790 Chapter 18 18.1 18.2 18.3 184 18.5 18.6 18.7 18.8 18.9 Appendix A Appendix B Appendix C Appendix D Appendix E Contents xvii Protection of Devices and Circuits 791 Introduction 791 Cooling and Heat Sinks 791 Thermal Modeling of Power Switching Devices 79 18.3.1 Electrical Equivalent Thermal Model 798 18.3.2 Mathematical Thermal Equivalent Circuit 800 18.3.3 Coupling of Electrical and Thermal Components 801 Snubber Circuits 803 Reverse Recovery Transients 804 Supply- and Load-Side Transients 810 Voltage Protection by Selenium Diodes and Metal Oxide Varistors 813 Current Protections 815 18.8.1 Fusing 815 18.8.2 Fault Current with AC Source 822 18.83 rault Current with DC Source 824 Electromagnetic Interference 827 18.91 SourcesofEMI | 828 18.92 Minimizing EMI Generation 828 189.3 EMI Shielding 829 18.9.4 EMI Standards 829 Summary 830 References 831 Review Questions 831 Problems 832 Three-Phase Circuits 835 Magnetic Circuits 839 Switching Functions of Converters 847 DC Transient Analysis 853 Fourier Analysis 857 Bibliography 860 Answersto Selected Problems 863 Index 871 Preface xxi gating signals for the power devices. Integrated circuits and discrete components are being replaced by microprocessors and signal processing ICs. An ideal power device should have no switching-on and -off limitations in terms of turn-on time, turn-off time, current, and voltage handling capabilities. Power semi- conductor technology is rapidly developing fast switching power devices with increas- ing voltage and current limits. Power switching devices such as power BJTs, power MOSFETS, SITs, IGBTs, MCT, SITHs, SCRs, TRIACs, GTOs, MTOs, ETOs, IGCTs, and other semiconductor devices are finding increasing applications in a wide range of products. With the availability of faster switching devices, the applications of modern microprocessors and digital signal processing in synthesizing the control strategy for gating power devices to meet the conversion specifications are widening the scope of power electronics. The power clectronies revolution has gained momentum, since the early 1990s, Within the next 20 years, power electronics will shape and condition the electricity somewhere between its generation and all its users. The potential applica- tions of power electronies are yet to be fully explored but we've made every effort to cover as many applications as possible in this book, Any comments and suggestions regarding this book are welcomed and should be sent to the author. Dr. Muhammad H. Rashid Professor and Director Electrical and Computer Engineering University of West Florida 11000 University Parkway Pensacola, FL 32514-5754 E-mail: mrashideuwtedu PSPICE SOFTWARE AND PROGRAM FILES The student version PSpice schematics and/or Orcad capture software can be obtained or downloaded from Cadence Design Systems, Inc, 2655 Seely Avenue San Jose, CA 95134 Websites: http://www.cadence.com http://www orcad.com http://www.pspice.com The website http:/uwtedumrashid contains all PSpice circuits, PSpice schematics, Orcad capture, and Mathcad files for use with this book. Important Note: The PSpice circuit files (with an extension .CIR) are self- contained and each file contains any necessary device or component models. However, the PSpice schematic files (with an extension .SCH) need the user-defined model li- brary file Rashid PE3 MODEL.LIB, which is included with the schematic files, and must be included from the Analysis menu of PSpice Schematics, Similarly, the Orcad xxii Preface schematic files (with extensions .OPJ and -DSN) need the user-defined model library file Rashid PE3 MODEL.LIB, which is included with the Orcad schematic files, must be included from the PSpice Simulation settings menu of Orcad Capture. Without these files being included while running the simulation, it will not run and will give errors. ACKNOWLEDGMENTS Many people have contributed to this edition and made suggestions based on their classroom experience as a professor or a student. 1 would like to thank the following persons for their comments and suggestions: lthas Mazen Abdel-Salam, King Fahd University of Petroleum and Minerals, Saudi Arabia Johnson Asumadu, Western Michigan University Ashoka K. SS. Bhat, University of Victoria, Canada Fred Brockhurst, Rose-Hulman Institution of Technology Jan C. Cochrane, The University of Melbourne, Australia Ovidiu Crisan, University of Houston Joseph M. Crowley, University of illinois, Urbana-Champaign Mehrad Ehsani, Texas A&M University Alexander E. Emanuel, Worcester Polytechnic Institute George Gela, Óltio State University Herman W. Hill, Ohio University Constantine J. Hatziadoniu, Southern Illinois University, Carbondale Wahid Hubbi, New Jersey Institute of Technology Marrija Iic-Spong, University of Iilinois, Urbana-Champaign Shahidul I. Khan, Concordia University, Canada Hussein M. Kojabadi, Sahand University of Technology, Iran Peter Lauritzen, University of Washington Jack Lawler, University of Tennessee Arthur R. Miles, North Dakota State University Medhat M. Morcos, Kansas State University Hassan Moghbelli, Purdue University Calumet H. Ramezani-Ferdowsi, University of Mashhad, fran Prasad Enjeti, Texas A&M University Saburo Mastsusaki, TDK Corporation, Japan Vedula V. Sastry, Jowa State University Elias G. Strangas, Michigan State University Selwyn Wright, The University of Huddersfield, Queensgate, UK S. Yuvarajan, North Dakota State University been a great pleasure working with the editor, Alice Dworkin and the production edi- tor, Donna King, Finally, | would thank my family for their love, patience, and understanding. MUHAMMAD H. RASHID Pensacola, Florida About the Author Muhammad H, Rashid received the B.Sc. degree in electrical engineering from the Bangladesh University of Engineering and Technology and the M.Sc. and Ph.D. de- grees from the University of Birmingham, UK. Currently, he is a Professor of electrical engineering with the University of Florida and the Director of the UF/UWE Joint Program in Electrical and Computer Engineer- ing. Previously, he was a Professor of electrical engineering and the Chair of the Engj- neering Department at Indiana University-Purdue University at Fort Wayne. In addition, he was a Visiting Assistant Professor of electrical engineering at the Univer- sity of Connecticut, Associate Professor of electrical engineering at Concordia Univer- sity (Montreal, Canada), Professor of electrical engineering at Purdue University, Calumet, and Visiting Professor of electrical engineering at King Fabd University of Petroleum and Minerals, Saudi Arabia. He has also been employed as a design and de- velopment engineer with Brush Electrical Machines Ltd. (UK), as a Research Engi- neer with Lucas Group Research Centre (UK), and as a Lecturer and Head of Control Engineering Department at the Higher Institute of Electronics (Malta), He is actively involved in teaching, researching, and lecturing in power electronics. He has published 14 books and more than 100 technical papers. His books have been adopted as text- books all over the world. His book Power Electronies has been translated into Spanish, Portuguese, Indonesian, Korcan and Persian. His book Microelectronics has been translated into Spanish in Mexico and Spain. He has had many invitations from foreign governments and agencies to be a keynote lecturer and consultant, from foreign uni- versities to serve as an external Ph.D. examiner, and from funding agencies to serve as a research proposal reviewer. His contributions in education have been recognized by foreign governments and agencies. He has previously lectured and consulted for NATO for Turkey in 1994, UNDP for Bangladesh in 1989 and 1994, Saudi Arabia in 1993, Pakistan in 1993, Malaysia in 1995 and 2002, and Bangkok in 2002, and has been invited by foreign universities in Australia, Canada, Hong Kong, India, Malaysia, Sin- gapore to serve as an external examiner for undergraduate, master's and Ph.D. degree examinations, by funding agencies in Australia, Canada, United States, and Hong Kong to review research proposals, and by U.S. and foreign universities to evaluate promo- tion cases for professorship. He has previously authored seven books published by Prentice Hall: Power Elecrronies—Circuits, Devices, and Applications (1988, 2/e 1993), SPICE For Power Electronics (1993), SPICE for Circuits and Electronics Using PSpice xiii 2 Chapter1 Introduction 11,1 Power Control [lie | Power MH equipment Static | Rotating Electronics Devices | Circuits Electronics FIGURE 1.1 Relationship of power electronies to power, electronics, and control. Power electronics have already found an important place in modern technology and are now used in a great variety of high-power products, including heat controls, light controls, motor controls, power supplies, vehicle propulsion systems, and high- voltage direct-current (HVDC) systems. It is difficult to draw the flexible ac transmis- sions (FACTSs) boundaries for the applications of power electronics, especially with the present trends in the development of power devices and microprocessors. Table 1.1 shows some applications of power electronics [5]. History of Power Electronics The history of power electronics began with the introduction of the mercury arc recti- fier in 1900. Then the metal tank rectifier, grid-controlled vacuum-tube rectifier, igni- tron, phanotron, and thyratron were introduced gradually. These devices were applied for power control until the 1950s. The first electronics revolution began in 1948 with the invention of the silicon transistor at Bell Telephone Laboratories by Bardeen, Brattain, and Schockley. Most of today's advanced electronic technologies are traceable to that invention. Modern mi- croelectronics evolved over the years from silicon semiconductors. The next break- through, in 1956, was also from Bell Laboratories: the invention of the PNPN triggering transistor, which was defined as a thyristor or silicon-controlled rectifier (SCR). The second electronics revolution began in 1958 with the development of the commercial thyristor by the General Electric Company. That was the beginning of a 1.1 Applications of Power Electronics TABLE 1.1 Some Applications of Power Electronics Advertising Aúir-conditioning Aircraft power supplies Alarms Appliances Audio amplifiers Battery charger Blenders Blowers Boilers Burglar alarms Cement kiln Chemical processing Clothes dryers Computers Conveyors Cranes and hoists Dimmers Displays Electric blankets Electric door openers Electric dryers Electric fans Electric vehicles Eleciromagneis Electromechanical electroplating Electronic ignition Electrastatic precipitators Elevators Fans Flashers Food mixers Food warmer trays Forklift trucks Furnaces Games Garage door openers Gas turbine starting Generator exciters Grinders Hand power tools Heat controls High-frequency lighting High-voltage de (HVDC) Induction heating Laser power supplics Latching relays Light dimmers Light flashers Linear induction motor controls Locomotives Machine tools Magnetic recordings Magnets Mass transits Mercury-are Lamp ballasts Mining Model trains Motor controls Mator drives Movie projectors Nuclear reactor control rod Oil well drilling Oven controls Paper milis Particle accelerators People movers Phonographs Photocopies Photographic supplies Power supplies Printing press Pumps and compressors Radar/sonar power supplies Range surface unit Refrigerators Regulators RF amplifiers Security systems Servo systems Sewing machines Solar power supplies Solid-state contactors Solid-state relays Space power supplies Static circuit breakers Static relays Steel mills Synchronous machine starting Synthetic fibers Television circuits Temperature controls Timers Toys Traffic signal controls Trains TV deflections Ultrasonic generators Uninterruptible power supplies Vacuum cleaners Volt-ampere reactive (VAR) compensation Vending machines Very low frequency (VLF) transmitters Voltage regulators Washing machines Welding Source: Rel 5. 3 (usudopaag pus queres 10] 11429 2assauta] jo Ásaino)) satuonaspo 1amod jo Most Ti aunoia e à + D at ç8t A - A Cem FIGUREIA & ee 1.2 Power Semiconductor Devices 7 4 e Various general-purpose diode configurations. (Counesy of Powerex, Inc.) thyristor, (1) emitter turn-off (ETO) thyristor, (j) integrated gate-commutated thyristor (IGCT), and (k) MOS-controlled thyristors (MCTs). Once a thyristor is in a conduc- tion mode, the gate circuit has no control and the thyristor continues to conduct. When a thyristor is in a conduction mode, the forward voltage drop is very small, typically 0.5 to 2 V.A conducting thyristor can be turned off by making the potential of the anode equal to or less than the cathode potential. The line-commutated thyristors are tumed off due to the sinusoidal nature of the input voltage, and forced-commutated thyristors are turned off by an extra circuit called commutation circuitry. Figure 1.5 shows various configurations of phase control (or line-commutated) thyristors: stud, hockey puck, flat, and pin types. Natural or line-commutated thyristors are available with ratings up to 6000 V, 4500 A. The turn-off time of high-speed reverse-blocking thyristors has been improved substantially and it is possible to have 10 to 20 us in a 3000-V, 3600-A thyristor. The turn- off time is defined as the time interval between the instant when the principal current has decreased to zero after external switching of the principal voltage circuit, and the in- stant when the thyristor is capable of supporting a specified principal voltage without “ a “ k E O ADE ES tmers CASS o O various thyristor configurations (Courtesy of Powerex, Inc.) 8 Chapterl | Introduction turning on. RCTs and GATTS are widely used for high-speed switching, especially in traction applications. An RCT can be considered as a thyristor with an inverse-parallel diode. RCTs are available up to 4000 V, 2000 A (and 800 A in reverse conduction) with a switching time of 40 us. GATTS are available up to 1200 V, 400 A with a switching speed of 8 us. LASCRs, which are available up to 6000 V, 1500 A, with a switching speed of 200 to 400 ps, are suitable for high-voltage power systems, especially im HVDC. For low-power ac applications, TRIACSs are widely used in all types of simple heat controls, light controls, motor controls, and ac switches. The characteristics ofTRIACSs are similar to two thyristors connected in inverse parallel and having only one gate termi- nal. The current flow through a TRIAC can be controlled in either direction. GTOs and SITHs are self-turned-off thyristors. GTOs and SITHs are turned on by applying a short positive pulse to the gates and are turned off by the applications of short negative pulse to the gates. They do not require any commutation circuit. GTOs are very atiractive for forced commutation of converters and are available up to 6000 V, 6000 A. SITHs, whose ratings can go as high as 1200 V,300 A, are expected to be applied for medium-power converters with a frequency of several hundred kilohertz and beyond the frequency range of GTOs. Figure 1.6 shows various configurations of GTOs. An MTO [3] is a combination of a GTO and a MOSFET, which together over- come the limitations of the GTO turn-off ability. Its structure is similar to that of a GTO and retains the GTO advantages of high voltage (up to 10 kV) and high current (up to 4000 A). MTOs can be used in high power applications ranging from 1 to 20 MVA. An ETO is a MOS-GTO hybrid device that combines the advantages of both the GTO and MOSFET. ETO has two gates: one normal gate for turn-on and one with a series MOSFET for turn-off ETOs with a current rating of up to 4 kA and a voltage rating of up to 6kV have been demonstrated. An IGCT [4] integrates a gate-commutated thyristor (GCT) with a multilayered printed circuit board gate drive. The GCT is a hard-switched GTO with a very fast and large gate current pulse, as large as the full-rated current, that draws out all the current from the cathode into the gate in about 1 us to ensure a fast turn-off. Similar to a GTO, FIGURE 1.6 Gate-turn-ofl thyristors (Courlesy of International Rectifiers.) 1.2.3 1.2 Power Semiconductor Devices 9 the IGCT is turned on by applying the turn-on current to its gate. The IGCT is turned off by a multilayered gate-driver circuit board that can supply a fast-rising turn-off pulse (i.e., a gate current of 4 kA/ps with gate-cathode voltage of 20 V only). An MCT can be turned “on” by a small negative voltage pulse on the MOS gate (with respect to its anode), and turned “off” by a small positive voltage pulse. It is like a GTO, except that the turn-off gain is very high. MCT' are available up to 4500 V, 250 A. Power Transistors Power transistors are of four types: (1) BJTs, (2) power MOSFETS, (3) IGBTS, and (4) SITs. A bipolar transistor has three terminals: base, emitter, and collector. It is normal- ly operated as a switch in the common-emitter configuration. As long as the base of an NPN-transistor is at a higher potential than the emitter and the base current is suffi- ciently large to drive the transistor in the saturation region, the transistor remains on, provided that the collector-to-emitter junction is properly biased. High-power bipolar transistors are commonly used in power converters at a frequency below 10 kHz and are effectively applied in the power ratings up to 1200 V, 400 A. The various configurations of bipolar power transistors are shown in Figure 4,2, The forward drop of a conducting transistor is in the range 0.5 to 1.5 V. If the base drive voltage is withdrawn, the transis- tor remains in the nonconduction (or off) mode. Power MOSFETS are used in high-speed power converters and are available at a relatively low power rating in the range of 1000 V,100 A at a frequency range of several tens of Kilohertz. The various power MOSFETS of different sizes are shown in Figure 4.24. IGBTs are voltage-controlled power transistors. They are inherently faster than BJTs, but still not quite as fast as MOSFETS. However, they offer far superior drive and output characteristics to those of BJTs. IGBTS are suitable for high voltage, high current, and frequencies up to 20 kHz. IGBTs are available up to 1700 V, 2400 A. COOLMOS [8] is a new technology for high-voltage power MOSFETS, and itim- plements a compensation structure in the vertical drift region of a MOSFET to im- prove the on-state resistance. It has a lower on-state resistance for the same package compared with that of other MOSFETS. The conduction losses are at least 5 times less as compared with those of the conventional MOSFET technology. COOLMOS is ca- pable of handling two to three times more output power as compared to the conven- tional MOSFET in the same package. The active chip area of COOLMOS is approximately 5 times smaller than that of a standard MOSFET. The on-state resis- tance of a 600'V, 47 A COOLMOS is 70 mf). A SITisa high-power, high-frequency device. It is essentially the solid-state ver- sion of the triode vacuum tube, and is similar to a junction field-effect transistor (JFET). It has a low-noise, low-distortion, high-audio-frequency power capability. The turn-on and turn-off times are very short, typically 0.25 us. The normally on-character- istic and the high ón-state drop limit its applications for general power conversions. The current rating of SITs can be up to 1200 V,300 A, and the switching speed can be as high as 100 kHz. SITs are most suitable for high-power, high-frequency applications (e.g. audio, VHFiultrahigh frequency [UHF], and microwave amplifiers). Figure 1.7 shows the power range of commercially available power semicon- ductors. The ratings of commercially available power semiconductor devices are shown in Table 1.2, where the on-voltage is the on-state voltage drop of the device at  TABLE 1.3 Characteristics and Symbols of Some Power Devices Devices Symbols Characteristics A K h v ps pm Dinde E 1,4) Gate triggered db e, v Thyristor A+ vao E 0 Me G sima app ox 1 q 1, Gute triggered ato tt a, v, Ao va. K o Lo AD OK MCT T Cathode Turnon Termott MTO gate eme Anade Cathode [— Tusn-ofl gate ETO 'Tum-on gate Arade Catbode Gate (turm-on de mare -oif) 16cr Ande 1 n 1 Ste triggered TRIAL qt fge— E Va A S Gate trigpered AM k n Srecgemea LusR dp b—s 7 n£ Lj h la Tu o eu a E= et o a Vez c v 4 h Lo tos erre ES ya im o E—— v; El: 1" Yes oh » to Vas NeChannel e E Vai Vu 08. y 5 p 1 a Vas mv sm | o io Vos 12 1.3 Control Characteristics of Power Devices 13 e, An ler car Es ca Current Product Range 100M == Future Devel. Plan 10M IM $ 1 sto +] ÃO E ok ristor ! 5 -.- 5 Teus i Sao pestia na Ele ué EE] forchemical |, ” dd HS AL] * f Retrigerator 100 TRIAÇ EM 88 05) PaehiDE jr condivoner Mieroeave een 10 tr 17 Ea U q 10 100 1K 10K 100K IM Operation frequency (Hz) FIGURE 1.8 Applications of power devices. (Courtesy of Powerex, Inc.) When a power semiconductor device is in a normal conduction mode, there is a small voltage drop across the device. In the output voltage waveforms in Figure 1.9, these voltage drops are considered negligible, and unless specified this assumption is made throughout the following chapters. La ana Ed The power semiconductor switching devices can be classified on the basis of: + Uncontrolled tum on and off (e.g,, diode); Controlled turn on and uncontrolled turn off (c.g., SCR); . Controlled turn-on and -off characteristics (c.g., BJT, MOSFET, GTO, SITH, IGBT, SIT, MCT); Continuous gate signal requirement (BJT, MOSFET, IGBT, SIT); Pulse gate requirement (e.g. SCR, GTO, MCT); Bipolar voltage-withstanding capability (SCR, GTO); Unipolar voltage-withstanding capability (BJT, MOSFET, GTO, IGBT, MCT); Bidirectional current capability (TRIAC, RCT); Unidirectional current capability (SCR, GTO, BJT, MOSFET, MCT, IGBT, SITH, SIT, diode). Table 1.4 shows the switching characteristics in terms of its voltage, current, and gate signals. 14 Chapter? Introduction Gate signal + Vo + + Input Thyristor Output voltage Re voltage V “o - - nt Tr! (b) GTO/MTO/ETOGCTIMCTISITH switch (For MCT, the polarity of Vg is reversed as shown) o 1 . + + - º " 4 TO! "e vi — V + R$ Bo -—————— 4 o 4 To! (e) Transistor switeh +oe— c D+ G o at el igBr qvos + bo 1 ams Pos E v $ o Y + + v Po R s Po - o | L., (d) MOSFET/TIGBT switch FIGURE 1.9 Control characteristics of power switching devices. 1.4 Characteristics and Specifications of Switches 17 11. Negative temperature coefficient on the conducted current is required to result in an equal current sharing when the devices are operated in parallel. 12. Low price is a very important consideration for reduced cost of the power elec- tronics equipment. 1.4.2 Characteristics of Practical Devices During the turn-on and -off process, a practical switching device, shown in Figure 1.10a, requires a finite delay time (1), rise time (t,), storage time (£,), and fall time (t,). As the device current i,, rises during tum-on, the voltage across the device v,, falls. As the de- vice current falls during turn-off, the voltage across the device rises. The typical wave- forms of device voltages vs and currents ico are shown in Figure 1,10b. The turn-on Nec Vw o Iows Eswo 0| ——— + vec js $ R < 0 isw ; + va ! io v, ! | / Vw Glsat) o vo switch (a) Controlled switch (b) Switch waveforms FIGURE 1.10 Typical waveforms of device voltages and currents. 18 143 Chapter 1 Introduction time (ton) of a device is the sum of the delay time and the rise time, whereas the turn- off time (tr) of a device is the sum of the storage time and the fall time. In contrast to an ideal, lossless switch, a practical switching device dissipates some energy when con- ducting and switching. Voltage drop across a conducting power device is at least on the order of 1 V, but can often be higher, up to several volts. The goal of any new device is to improve the limitations imposed by the switching parameters. The average conduction power loss, Pon is given by tom Pn=— pdt (11) Todo where Tg denotes the conduction period and p is the instantancous power loss (ie., product of the voltage drop v,, across the switch and the conducted current içe). Power losses increase during turn-on and turn-off of the switch because during the transition from one conduction state to another state both the voltage and current have signifi- cant values. The resultant switching power loss Psy during the turn-on and turn-off pe- riods, is given by Pow =1( [par + fra + [pai (12) fs = WTs is the switching frequency: t,, t,, and f, are the rise time, storage time, and fall time respectively. Therefore, the power dissipation of a switching device is given by: Pp = Pon + Pow + Fa (1.3) where Pg is the gate driver power. Switch Specifications The characteristics of practical semiconductor devices differ from those of an ideal de- vice. The device manufacturers supply data sheets describing the device parameters and their ratings. There are many parameters that are important to the devices. The most important among these are: Valtage ratings: Forward and reverse repetitive peak voltages, and an on-state forward voltage drop. Current ratings: Average, root-mean-square (rms), repetitive peak, nonrepetitive peak, and off-state leakage currents. Switching speed or frequency: Transition from a fully nonconducting to a fully conducting state (turn-on) and from a fully conducting to a fully nonconducting state (turn-off) are very important parameters. The switching period Ts and fre- quency fs are given by 1 l Ds >>> + 0 14 5 To tt EI tor (4) where tog is the off time during which the switch remains off. 1.4 Characteristics and Specifications of Switches 19 difdt rating: The device needs a minimum amount of time before its whole con- ducting surface comes into play in carrying the full current. If the current rises rapidly, the current flow may be concentrated to a certain area and the device may be damaged. The didt of the current through the device is normaily limited by connecting a small inductor in series with the device, known as a series smuebber, duldt rating: A semiconducior device has an internal junction capacitance C;. 1f the voltage across the switch changes rapidly during turn-on, turn-off and also while connecting the main supply the initial current, the current €; dv/dt flowing through €; may be too high, thereby causing damage to the device, The dvldr of the voltage across the device is limited by connecting an RC circuit across the de- vice, known as a shunt snubber, or simply snubber. Switching losses: During turn-on the forward current rises before the forward voltage falls, and during turn-off the forward voltage rises before the current falls. Simultaneous existence of high voltage and current in the device represents power losses as shown in Figure 1.10b. Because of their repetitiveness, they rep- resent a significant part of the losses, and often exceed the on-state conduction losses. Gate drive requirements: The gate-drive voltage and current are important pa- rameters to turn-on and -off a device, The gate-driver power and the energy re- quirement are very important parts of the losses and total equipment cost. With large and long current pulse requirements for turn-on and turn-off, the gate drive losses can be significant in relation to the total losses and the cost of the driver circuit can be higher than the device itself. Safe operating area (SOA): The amount of heat generated in the device is pro- portional to the power loss, that is, the voltage-current product. For this product to be constant P = vi and equal to the maximum allowable value, the current must be inverse proportional to the voltage. This yields the SOA limit on the al- lowable steady-state operating points in the voltage-current coordinates, Tt for fusing: This parameter is needed for fuse selection. The It of the device must be less than that of the fuse so that the device is protected under fault cur- rent conditions. Temperatures: Maximum allowable junction, case and storage temperatures, usu- ally between 150ºC and 200ºC for junction and case, and between =50"C and 175ºC for storage. Thermal resistance: Junction-to-case thermal resistance, Oc; case-to-sink ther- mal resistance, Qcs: and sink-ambient thermal resistance. Os 4. Power dissipation must be rapidly removed from the internal wafer through the package and ulti- mately to the cooling medium. The size of semiconductor power switches is small, not exceeding 150 mm, and the thermal capacity of a bare device is too low to safely remove the heal generated by internal losses. Power devices are generally mounted on heat sinks. Thus, removing heat represents a high cost of equipment. 1.4.4 Device Choices Although, there are many power semiconductor devices, nonc of them have the ideal characteristics. Continuous improvements are made to the existing devices and new 22 Chapter1 Introduction TRIAC v, = Vo Sinto vs ae supply o (a) Circuit diagram (b) Voltage waveforms FIGURE 1.13 Single-phase ac-ac converter. Static switches. Because the power devices can be operated as static switches or contactors, the supply to these switches could be either ac or de and the switches are called as ac static switches or de switches. A number of conversion stages are often cascaded to produce the desired output as shown in Figure 1.16, Mains 1 supplies the normal ac supply to the load through the static bypass. The ac-dc converter charges the standby battery from mains 2. The de-ac + Por Transistor l “ % o E + = t Vo ba Ve Ns 0 4 T t (a) Circuit diagram (b) Voltage waveforms FIGURE 1.14 De-de converter. 1.6 Design of Power Electronics Equipment 23 Pato pa + T ' q mw A 7H T TO! de “a Po 2 bg Load | supply + Loa Vo HH IT T t pa (] z (a) Circuit diagram (b) Voltage waveforms FIGURE 1.15 Single-phase de-ac converter. converter supplies the emergency power to the load through an isolating transformer. Mains 1 and mains 2 are normally connected to the same ac supply. 1.6 DESIGN OF POWER ELECTRONICS EQUIPMENT The design of a power electronics equipment can be divided into four parts: 1. Design of power circuits 2. Protection of power devices 3. Determination of control strategy 4. Design of logic and gating cireuits Mains 1 | Load Mains 2 — Nu Isolati e by Rectificricharger Inverter rare Slate ypass Battery FIGURE 1.16 Block diagram of an uninterruptible power supply (UPS). 24 Chapter | Introduction Inthe chapters that follow, various types of power electronic circuits are described and analyzed. In the analysis, the power devices are assumed to be ideal switches unless stated otherwise; and effects of circuit stray inductance, circuit resistances, and source inductance are neglected. The practical power devices and circuits differ from these ideal conditions and the designs of the circuits are also affected, However, in the early stage of the design, the simplified analysis of a circuit is very useful to understand the operation of the circuit and to establish the characteristics and control strategy. Before a prototype is built, the designer should investigate the effects of the cir- cuit parameters (and devices imperfections) and should modify the design if necessary. Only after the prototype is built and tested, the designer can be confident about the va- lidity of the design and can estimate more accurately some of the circuit parameters (ep. stray inductance). DETERMINING THE ROOT-MEAN-SQUARE VALUES OF WAVEFORMS To accurately determine the conduction losses in a device and the current ratings of the device and components, the rms values of the current waveforms must be known. The current waveforms are rarely simple sinusoids or rectangles, and this can pose some problems in determining the rms values. The rms value of a waveform i(t) can be calculated as + Los = Tl P dr (1.5) where T is the time period. If a waveform can be broken up into harmonics whose rms values can be calculated individually, the rms values of the actual waveform can be ap- proximated satisfactorily by combining the rms values of the harmonies. That is, the rms value of the waveform can be calculated from as = Me E Pasto) E as) É E Lema) (1.6) where ly = the de component. Iys(1) ANd Ims(n) Are the rms values of the fundamen- tal and nth harmonic components, respectively. Figure 1.17 shows the rms values of different waveforms that are commonly en- countered in power electronics. PERIPHERAL EFFECTS The operations of the power converters are based mainly on the switching of power semiconductor devices; and as a result the converters introduce current and voltage harmonics into the supply system and on the output of the converters. These can cause problems of distortion of the output voltage, harmonic generation into the supply sys- tem, and interference with the communication and signaling circuiís. It is normally nec- essary to introduce filters on the input and output of a converter system to reduce the 1.10 Intelligent Modules 27 output isolation from, and interface with, the signal and high-voltage system, a drive circuit, a protection and diagnostic circuit (against excess current, short circuit, an open load overheating, and an excess voltage), microcomputer control, and a control power supply. The users need only to connect external (floating) power supplies. An intelli- gent module is also known as smart power. These modules are used increasingly in power electronics [6]. Smart power technology can be viewed as a box that interfaces power source to any load. The box interface function is realized with high-density complementary metal oxide semiconductor (CMOS) logic circuits, its sensing and protection function with bipolar analog and detection circuits, and its power control function with power devices and their associated drive circuits. The functional block di- agram of a smart power system [7] is shown in Figure 1.19. The analog circuits are used for creating the sensors necessary for self-protection and for providing a rapid feedback loop, which can terminate chip operation harmlessly when the system conditions exceed the normal operating conditions. For example, smart power chips must be designed to shut down without damage when a short circuit occurs across a load such as a motor winding. With smart power technology, the load current is monitored, and whenever this current exceeds a preset limit, the drive voltage to the power switches is shut off. In addition to this over-current protection features such as Smart power technology Bipolar power transistors Power Insulated-gate bipolar transistors| Power Solrol MOS-controlled ihyristors Drive | r[30-Y CMOS Cuits o Figh-voltage level shift Analog | pfHigh-speed bipolar transistors eircuits pm Operational amplifiers Sensing and ct Overvoltage/undervoltage Overtempera Overcurrent'no-load a * |] Interface + cdreults High-density O: FIGURE 1.19 Functional block diagram of a smart power. [Reí. 7, 1 Baliga] 28 Chapter 1 Introduction overvoltage and overtemperature protection are commonly included to prevent de- structive failures. Some manufacturers of devices and modules and their Web sites are as follows: Advanced Power Technology, Inc. ABB Semiconductors Eupec Fuji Electric Collmer Semiconductor, Inc, Dynex Semiconductor Harris Corp. Hitachi, Ltd. Power Devices Infineon Technology International Rectifier Marconi Electronic Devices, Inc. Mitsubishi Semiconductors Mitel Semiconductors Motorola, Inc. National Semiconductors, Inc. Nihon International Electronics Corp. On Semiconductor Philips Semiconductors Power Integrations, Inc. Powerex, Inc. Power Tech, Inc. RCA Corp. Rockwell Inc. Reliance Electric Siemens Silicon Power Corp. Semikron International Siliconix, Inc. Tokin, Inc. Toshiba America Electronic Components, Inc. Unitrode Integrated Circuits Corp. Westeode Semiconductors Ltd. wwwadvancedpower.com/ www abbsem.com/ wwweupec.com/p/index.him www fujielectric.co,jp/eng/denshi/scd/index.htm wwwcollmer.com wwwdynexsemi.com wwwharris.com/ www.hitachi.co.jp/pse www.infineon.com/ wwwiricom www.marconi.com/ www mitsubishiclectric.com/ wwwmitelsemi.com wwwmotorolacom wwwnational.com/ www abbsem.com/english/salesb.htm www onsemi.com wwwsemiconductors.philips.com/catalog/ www. powerint.com/ wwwpwrx.com/ www.power-tech.com/ wwwrca.com/ www.rockwell.com www reliance.com www.siemens.com wwwsiliconpower.com/ www.semikron.com/ wwwsiliconix.com www.tokin.com/ www.toshiba.com/tace/ www unitrode.com/ wwwwestcode.com/ws-prod.html POWER ELECTRONICS JOURNALS AND CONFERENCES There are many professional journals and conferences in which the new develop- ments are published. The Institute of Electrical and Electronics Engineers (IEEE) e-library Explore is an excellent tool in finding articles published in the IEE journals References 29 and magazines, and in the IEEE journals, magazines, and sponsored conferences. Some of them are: IEEE e Library iecexplore.iece.org/ IEEE Transactions on Aerospace und Systems www.jece.org/ IEEE Transactions on Indusírial Electronics wwmece.org/ TEEE Transactions on Industry Applications www.lece.org/ TEEE Transactions on Power Delivery www ece.org/ JEEE Transactions on Power Electronics www.icec.org/ IEE Proceedings on Electric Power www.iee.org/Publish/ Joumal of Electrical Machinery and Power Systems Applied Power Electronics Conference (APEC) European Power Electronics Conference (EPEC) TEEE Industrial Electronics Conference (TECON) TEEE Industry Applications Society (1AS) Annual Meeting International Conference on Electrical Machines (ICEM) International Power Electronics Conference (IPEC) International Power Electronics Congress (CIEP) International Telecommunications Energy Conference (INTELEC) Power Conversion Intelligent Motion (PCIM) Power Electronics Specialist Conference (PESC) SUMMARY As the technology for the power semiconductor devices and integrated circuits devel- ops, the potential for the applications of power electronics becomes wider, There are already many power semiconductor devices that are commercially available; however, the development in this direction is continuing. The power converters fall generally into six categories: (1) rectifiers, (2) ac-de converters, (3) ac-ac converters, (4) de-de converters, (5) de-ac converters, and (6) static switches. The design of power electron- ics circuits requires designing the power and control circuits. The voltage and current harmonics that are generated by the power converters can be reduced (or minimized) with a proper choice of the control strategy. REFERENCES [1] E.L Carroll,“Power electronics: where next?” Power Engineering Journal, December 1996, pp. 242-243. [2] S.Bernct, “Recent developments of high power converters for industry and traction appli- cations” JEEE Transactions on Power Electronies, Vol. 15, No. 6, November 2000, pp. 1102-1117. [3] E. Carroll “Power electronies for very high power applications) Power Engineering Jour- nat, April 1999, pp. 81-87. [4] PXK.Steimer, H. E. Gruning, J. Werninger, E. Carroll, S. Klada, and S. Linder, “IGCT—a new emerging for high power, low cost inverters” JEEE Industry Applications Magazine, July/August 1999, pp. 12-18. [5] R.G Hoft, Semiconductor Power Electronics. New York: Van Nostrand Reinhold. 1986. 32 Chapter? Power Semiconductor Diodes and Circuits grown in the so-called float zone furnaces. Each huge crystal is sliced into thin wafers, which then go through numerous process steps to turn into power devices. Silicon, is a member of Group IV of the periodie table of elements, that is, hav- ing four electrons per atom in its outer orbit. A pure silicon material is known as an imtrinsic semiconducior with resistivity that is too low to be an insulator and too high to be a conductor. It has high resistivity and very high dielectric strength (over 200 kV/cm). The resistivity of an intrinsic semiconductor and its charge carriers that are available for conduction can be changed, shaped in layers, and graded by im- plantation of specific impurities. The process of adding impurities is called doping, which involves a single atom of the added impurity per over a million silicon atoms. With different impurities, levels and shapes of doping, high technology of photolith- ography, laser cutting, etching, insulation, and packaging, the finished power devices are produced from various structures of n-type and p-type semiconductor layers. n-Type material: If pure silicon is doped with a small amount of a Group V ele- ment, such as phosphorus, arsenic, or antimony, each atom of the dopan! forms a covalent bond within the silicon lattice, leaving a loose electron, These loose elec- trons greatly increase the conductivity of the material. When the silicon is lightly doped with an impurity such as phosphorus, the doping is denoted as n doping and the resultant material is referred to as n-type semiconductor. When itis heav- ily doped, it is denoted as n+ doping and the material is referred to as n+-type semiconductor. p-Type material: If pure silicon is doped with a small amount of a Group III cle- ment, such as boron, gallium, or indium, a vacant location called a hole is intro- duced into the silicon lattice. Analogous to an electron, a hole can be considered a mobile charge carrier as it can be filled by an adjacent electron, which im this way leaves a hole behind. These holes greatly increase the conductivity of the ma- terial. When the silicon is lightly doped with an impurity such as boron, the dop- ing is denoted as p-doping and the resultant material is referred to as p-type semiconductor. When it is heavily doped, it is denoted as p+ doping and the ma- terial is referred to as p+-type semiconductor. Therefore, there are free clectrons available in an n-type material and free holes avail- able in a p-type material. In a p-type material the holes are called the majority carriers and electrons are called the minority carriers, In the n-type material, the electrons are called the majority carriers, and holes are called the minority carriers. These carriers are continuously generated by thermal agitations, they combine and recombine in ac- cordance to their lifetime, and they achieve an equilibrium density of carriers from about 10º to 10/%/cmº over a range of about O “C to 1000 “C. Thus, an applied electric field can cause a current flow in an n-type or p-type material, Key Points of Section 2.2 * Free electrons or holes are made available by adding impurities to the pure sili- con or germanium through a doping process. The electrons are the majority carri- ers in the n-typc material whercas the holes are the majority carriers in a p-Lype 23 2.3 Diode Characteristics 33 material, Thus, the application of electric field can cause a current flow in an n-type or a p-type material, DIODE CHARACTERISTICS A power diode is a two-terminal pr-junction device [1,2] and a pr-junction is nor- mally formed by alloying, diffusion, and epitaxial growth. The modern control tech- niques in diffusion and epitaxial processes permit the desired device characteristics. Figure 2.1 shows lhe sectional view of a pn-junction and diode symbol. When the anode potential is positive with respect to the cathode, the diode is said to be forward biased and the diode conducts. A conducting diode has a rela- tively small forward voltage drop across it; and the magnitude of this drop depends on the manufacturing process and junction temperature. When the cathode potential is positive with respect to the anode, the diode is said to be reverse biased. Under reverse-biased conditions, a small reverse current (also known as leakage current) in the range of micro- or milliampere, flows and this leakage current increases slowly in magnitude with the reverse voltage until the avalanche or zener voltage is reached. Figure 2.2a shows the steady-state v—i characteristics of a diode. For most practical purposes, a diode can be regarded as an ideal switch, whose characteristics are shown in Figure 2.2b. The v-i characteristics shown in Figure 2.2a can be expressed by an equation known as Schocktey diode equation, and it is given under de steady-state operation by tp = I(elento — 1) (21) where Ip = current through the diode, A; Vo = diode voltage with anode positive with respect to cathode, V; 1, = leakage (or reverse saturation) current, typically in the range 107f to IO A; n = empirical constant known as emission coefficieni, or ideality factor, whosc value varics from 1 to 2. The emission coefficient depends on the material and the physical construction of the diode. For germanium diodes, n is considered to be 1. For silicon diodes, the pre- dicted value of n is 2, but for most practical silicon diodes, the value of n falls in the range 1.1 to 1.8. Anode Cathode Anode Cathode ln - D+ i i Dr . Vl P. + + tt FIGURE 2.1 (a) pajunction (b) Diode symbol pn-Junction and diode symbol 34 Chapter? Power Semiconductor Diodes and Circuits lp —Vor L | “o ! I [ o v é 1 Reverse leakage current FIGURE 2.2 (a) Practical (b) Ideal vi Characteristics of diode. Vr in Eq. (2.1) is a constant called thermal voltage and it is given by =s&T v; "q (2.2) where q = electron charge: 1.6022 x 10” coulomb (C); T = absolute temperature in Kelvin (K = 273 + *C); k = Boltzmann's constant: 1.3806 x 102 J/K. Ata junetion temperature of 25 ºC, Eq. (2.2) gives o KT 13806 x 10? x (273 + 25) =35ImV Tg 1.6022 x 1079 Sdim Ata specified temperature, the leakage current 1, is a constant for a given diode, The diode characteristic of Figure 2.2a can be divided into three regions: Forward-biased region, where Vp > O Reverse-biased region, where Vp < O Breakdown region, where Vp < —Vax Forward-biased region. In the forward-biased region, Vp > 0. The diode cur- rent Tp is very small if the diode voltage Vp is less than a specific value Vrp (typically 0.7 V). The diode conducts fully if Vp às higher than this value Vrp, which is referred to as the threshold voltage, cut-in voltage, or turn-on voltage. Thus, the threshold voltage is a voltage at which the diode conducts fully. Let us consider a small diode voltage Vp = 01V,n =, and Vr=257mV. From Eg. (2.1) we can find the corresponding diode current Ip as fo = Eee — 1) = A [eMUMICS) — 1) = 1,(4896 — 1) = 47,961, which can be approximated to Ip = Lelo'nto = 48.96 1, that is, wilh an error of 2.1%. As vp increases, the error decreases rapidly. 24 Reverse Recovery Characteristics 37 Equating Jar in Eq. (2.6) 10 Jay in Eq. (2.8) gives — 20nr furta = ride (2.9) MH 4y is negligible as compared to 1, which is usually the case, [,, = ty, and Eq. (2.9) becomes (20rr er É NV aitar (210) and tmn =a 2a (241) Ttcan be noticed from Egs. (2.10) and (2.11) that the reverse recovery time t,, and the peak reverse recovery current Ia depend on the storage charge Op and the reverse (or reapplied) di/dt. The storage charge is dependent on the forward diode current fp. The peak reverse recovery current /pp, reverse charge Q rx, and the SF are all ofinter- estto the circuit designer, and these parameters are commonly included in the specifi- cation shects of diodes. If a diode is in a reverse-biased condition, a leakage current flows due to the mi- nority carriers. Then the application of forward voltage would force the diode to carry current in the forward direction. However, it requires a certain time known as forward recovery (or tum-on) time before all the majority carriers over the whole junction can contribute to the current flow. If the rate of rise of the forward current is high and the forward current is concentrated to a small arca of the junction, the diode may fail. Thus, the forward recovery time limits the rate of the rise of the forward current and the switching speed. Example 2.2 Finding the Reverse Recovery Current The reverse recovery time of a diode is 1, = 31s and the rate of fall of the diode current is ditdt = 30 A/ps. Determine (a) the storage charge Ox, and (b) the peak reverse current Ira. Solution ty = 3 ps and ditdt = 30 Alps. a. From Eq. (12.10), i 2 = 05x 30A/nsx (3x 10% = 1359C Om = b. From Eg. (2.11), Ian = an = 2 x 135 X 10º x 30 x 10º = 90 A 38 Chapter2 Power Semiconductor Diodes and Circuits 25 2.51 2.5.2 Key Points of Section 2.4 * During the reverse recovery time r,,, the diode behaves effectively as a short cir- cuit and is not capable of blocking reverse voltage, allowing reverse current flow, and then suddenly disrupting the current. Parameter (,, is important for switching applications. POWER DIODE TYPES Ideally, a diode should have no reverse recovery time. However, lhe manufacturing cost of such a diode may increase. In many applications, the effects of reverse recovery lime is not significant, and inexpensive diodes can be used. Depending on the recovery characteristics and manufacturing techniques, the power diodes can be classificd into the following three categories: 1. Standard or general-purpose diodes 2. Fast-recovery diodes 3, Schottky diodes The characteristics and practical limitations of these types restrict their applications. General-Purpose Diodes The general-purpose reclifier diodes have relatively high reverse recovery time, typi- cally 25 us; and are used in low-speed applications, where recovery time is not critical (e.g. diode rectifiers and converters for a low-input frequency up to 1-kHz applications and line-commutated converters). These diodes cover current ratings from less than 1A to several thousands of amperes, with voltage ratings from 50 V to around 5 KV. These diodes are generally manufactured by diffusion. However, alloyed types of recti- fiers that are used in welding power supplies are most cost-cffective and rugged, and their ratings can go up to 1500 V, 400 A. Figure 2.4 shows various configurations of general-purpose diodes, which basi- cally fall into two types. One is called a stwd, or stud-mounted type; the other one is called a disk, press pak,or hockey-puck type. In a stud-mounted type. either lhe anode or the cathode could be the stud, Fast-Recovery Diodes The fast-recovery diodes have low recovery time, normally less than 5 ps. They are used in de-de and de-ac converter circuits, where the speed of recovery is often of critical importance. These diodes cover current ratings of voltage from 50 V to around 3kV, and from less than 1 A to hundreds of amperes. For voltage ratings above 400 V, fast-recovery diodes are generally made by dif- fusion and the recovery time is controlled by platinum or gold diffusion. For voltage ratings below 400 V, epitaxial diodes provide faster switching speeds than those of dif- Tused diodes. The epitaxial diodes have a narrow base width, resulting in a fast recovery time of as low as 50 ns. Fast-recovery diodes of various sizes are shown in Figure 2.4. 2.6 Silicon Carbide Diodes 39 FIGURE 2.4 ] Fast-recovery diodes. (Courtesy of Powerex, Inc.) 2.5.3 Schottky Diodes 2.6 The charge storage problem of a pn-junction can be eliminated (or minimized) in a Schottky diode. It is accomplished by setting up a “barrier potential” with a contact be- tween a metal and a semiconductor. À layer of metal is deposited on a thin epitaxial layer of n-type silicon. The potential barrier simulates the behavior of a pn-junetion. The rectifying action depends on the majority carriers only, and as a result there are no excess minority carriers to recombine. The recovery effect is due solely to the self- capacitance of the semiconductor junction. The recovered charge of a Schottky diode is much less than that of an equiva- lent pn-junction diode. Because it is due only to the junction capacitance, il is largely independent of the reverse difdt. A Schottky diode has a relatively low forward volt- age drop. The“leakage current of a Schottky diode is higher than that of a pn-junction diode. A Schottky diode with relatively low-conduction voltage has relatively high leakage current, and vice versa. As a result, the maximum allowable voltage of this diode is generally limited to 100 V. The current ratings of Schottky diodes vary from 1 to 400 A. The Schottky diodes are ideal for high-current and low-voltage de power sup- plies. However, these diodes are also used in low-current power supplies for increased efficiency. In Figure 2.5, 20- and 30-A dual Schottky rectifiers are shown. Key Points of Section 2.5 * Depending on the switching recovery time and the on-state drop, the power diodes are of three types: general purpose, fast recovery, and Schottky. SILICON CARBIDE DIODES Silicon Carbide (SiC) is a new material for power electronics. Its physical properties outperform Si and GaAs by far. For example, the Schottky SiC diodes manufactured 42 Chapter2 Power Semiconductor Diodes and Circuits 2.8 SERIES-CONNECTED DIODES In many high-voltage applications (e.g., high-voltage direct current [HVDC] transmis- sion lines), one commercially available diode cannot meet the required voltage rating, and diodes are connected in series to increase the reverse blocking capabilities. Let us consider two series-connected diodes as shown in Figure 2.7a, Variables ip and vp are the current and voltage, respectively, in the forward direction; vp; and Yna are the sharing reverse voltages of diodes D, and D», respectively. In practice, the vi characteristics for the same type of diodes differ due to tolerances in their pro- duction process. Figure 2.7b shows two v—j characteristics for such diodes. In the for- ward-biased condition, both diodes conduct the same amount of current, and the forward voltage drop of each diode would be almost equal. However, in the reverse blocking condition, ech diode has to carry the same leakage current, and as a result the blocking voltages may differ significantly, A simple solution to this problem, as shown in Figure 2.8a, is to force equal volt- age sharing by connecting a resistor across each diode. Due to equal voltage sharing, the leakage current of each diode would be different, and this is shown in Figure 2.8b. Because the total leakage current must be shared by a diode and ils resistor, L=la+tlm=to+ to (212) However, fm = Voy/'Ry and lg = Vo!R, = Vyy'R>. Equation (2.12) gives the rela- tionship between Rj and R; for equal voltage sharing as Vo Vir tato Sta t Rs (2.13) If the resistances are equal, then R = Rj = R; and the two diode voltages would be slightly different depending on the dissimilarities of the two v—i characteristics. The Yo Yom Po (a) Circuit diagram (b) v-i Characteristics FIGURE 2.7 Two series-connected diodes with reverse bias. 2.8 Series-Connected Diodes 43 (a) Circuit diagram (b) u-i Characteristics FIGURE 2.8 Series-connected diodes with steady-state voltage-sharing characteristics, Send je E Transient voltage voltage sharing Sharing FIGURE 29 Series diodes with voltage-sharing networks under steady-state and transient conditions. values of Vpy and Vpz can be determined from Eys. (2.14) and (2.15): v, lt =t+ 214 ta 2 (2.14) Vo + Vin = V (2.15) The voltage sharimgs under transient conditions (e.g., due to switching loads, the ini- tial applications of the input voltage) are accomplished by connecting capacitors across cach diode, which is shown in Figure 2.9. R, limits the rate of rise of the block- ing voltage. Example 2.3 Finding the Voltage Sharing Resistors Two diodes are connected in series, shown in Figure 2.8a to share a total de reverse voltage of Vo = 5kV. The reverse leakape currents of the two diodes are 4, = 30 mA and Ly = 35 mA. (a) Find the diode voltages if the volt haring resistances are equal, R, = R= 0KkN (b) Find the voltage-sharing resistances R, and Ro if lhe diode voltages are equal, Voy = Vo = Vp/2. (e) Use PSpice to check your results of part (a). PSpice model parameters of the diodes are BV = 3 kV and IS = 30mA for diode D,, and IS 5 mA for diade D. 44 Chapter2 Power Semiconductor Diodes and Circuits Solution a = 30mA,lo=35mA, and Rj=R,=R=10kM -Vp=-Fh—Vo o Voa = Vo — For From Eq. (2.14), MH Vm Int p= lar R Substituting Voz = Vp — Vpy and solving for the diode voltage Dy, we get W.R Vo = tala ha) = se + a (35 x 10? — 30 x 107) = 2750V (2.16) and Vo = Vo — Va = 5kV — 2750 = 2250V, b. 11 =30MA, La = 35mA, and Vo = Vo = Vo2 = 2.5kV. From Eg. (2.13), Yo + Ym to 2 which gives the resistance Rs for a known value of R, as VR m= mfty CO Vo Rilo— Ia) Cm Assuming that R, = 100k9, we get 5 KV. R 25kV x I00k0 = TED in = 135kt) É 2.5kV — 100k0 x (35 x 10? — 30 x 107) e The diode circuit for PSpice simulation is shown in Figure 2.10, The list of the circuit file is as follows: Example 2.3 Diode Voltage-Sharing Circuit vs 1 o pe SKv R 1 2 0.01 Rê 2 3 100K R2 3 o 100K DI 3 2 MODI DR 0 3 MODZ MODEL MODI D (15=30MA BV=3KV) : Diode model parameters «MODEL MODZ D (15=35MA BV=3KV) ; Diode model parameters .oP ; Dc operating point analysis «END 2.10 Diodes with RCand RL Loads 47 With initial condition u.(t = 0) = 0, the solution of Eq. (2.18) (which is derived in Ap- pendix D, Eg. D.1) gives the charging current i as Y (o) = Re” (2.20) The capacitor voltage v, is t vt) = E [ia =WIl ce! =V(- e") (2.21) where 7 = RC is the time constant of an RC load. The rate of change of the capacitor voltage is du Vo are da RCº (2:22) and the initial rate of change of the capacitor voltage (at 1 = 0) is obtained from Eq. (2.22) dep Mo dtl-o RC A diode circuit with an RL load is shown in Figure 2.13a.When switch $, is closed att = 0, the current i through the inductor increases and is expressed as (2.23) di K=wtu=LT+ Ri (2.24) With initial condition i(t = 0) = 0, the solution of Eq. (2.24) (which is derived in Appendix D, Eq. D.2) yields = Eu — eRiL) (2.25) (a) Circuit diagram (b) Waveforms FIGURE 2.13 Diode circuit with an RL load. 48 Chapter2 | Power Semiconductor Diodes and Circuits The rate of change of this current can be obtained from Eg. (2.25) as di ara uz (2.26) and the initial rate of rise of the current (att = 0) is obtained from Eg. (2.26): dio V dilieo o L (227) The voltage v, across the inductor is vilt) = LE = = WetRil (2.28) where L/R = 7 is the time constant of an RL load. The waveforms for voltage v and current are shown in Figure 2.13b. Tf 1 >> LIR, the voltage across the inductor tends to be zero and its current reaches a steady-state value of 1, = W/R. If an attempt is then made to open switch 5,, the energy stored in the inductor (= 0.5Li?) will be transformed into a high reverse voltage across the switch and diode. This energy dissipates in the form of sparks across lhe switch; and diode Dy is likely to be damaged in this process. To overcome such a situation, a diode commonly known as a freewheeling diode is connected across an inductive load as shown in Figure 2.21a. Note: Because the current i in Figures 2.12a and 2.13a is unidirectional and does not tend to change its polarity, the diodes have no effect on circuit operation. Key Points of Section 2.10 * The current of an RC or RL circuit that rises or falls exponentially with a circuit time constant does not reverse its polarity. The initial dv/dt of a charging capaci- tor in an RC circuit is VK/RC, and the initial difdrin an RL circuit is Vy/L. Example 2.4 Finding the Peak Current and Energy Loss in an RC Circuit A diode circuit is shown in Figure 2.14a with R = 44 fland€ = 0.1 gF.The capacitor has an ini- tial voltage, Vo = Vit = 0) = 220 V, If switch S, is closed at ! = 0, determine (a) the peak diode current, (b) the energy dissipated in the resistor R, and (c) the capacitor voltage at t=2ys. Solution The waveforms are shown in Figure 2.14b. à. Equation (2.20) can be used with V, = Vo and the peak diode current [, is b. The energy W dissipated is W = 05CVi = 050.1 x 10x 220º = 000242] =242m] 2.11 | Diodes with LCand RLC Loads 49 vo fé R o t vo RE o t (a) Circuit diagram (b) Waveforms FIGURE 2.14 Diode cireuit with an RC load. e ForRC=4 x0lu=44usandr=1=ã2us, the capacitor voltage is ult=2p8) = Vigo 80 = 220 x et = 139,64 V Note: Because the current is unidirectional, the diode does not affect circuit operation. 2.11 DIODES WITH LC AND RLC LOADS A diode circuit with an LC load is shown in Figure 2.15a. The source voltage V is a de constant voltage, When switch 5, is closed att = 0, the charging current í of the capac- itor is expressed as di Rolf n=Lite [ide + ut =0) (2.29) (a) Circuit diagrams (b) Waveforms FIGURE 2.15 Diode circuit with an LC load. 52 Chapter2 Power Semiconductor Diodes and Circuits + FIGURE 2.17 E fe % Diode circuit with an RLC load. —. Under final steady-state conditions, the capacitor is charged to the source voltage V, and the steady-state current is zero. The forced component of the current in Eg. (2.37) is also zero. The current is due to the natural component. “The characteristic equation in Laplace's domain of s is (2.38) (2.39) Lei us define two important properties of a second-order circuit: the damping factor, R e= (2.40) and the resonant frequency, 1 =——— 2.41 “= LE (2.41) Substituting these into Eg. (2.39) vields s2=-a+NV o — qj (2.42) The solution for the current, which depends on the values of a and wo, would follow one of'the three possible cases. Case 1. lfa = , the rools are equal, sy = s,, and the circuit is called eritically damped. The solution takes the form HO) =(4, + Ape" (2.43) Case 2. Ifa > ay, the roots are real and the circuit is said to be over-damped. The solution takes the form to) = Ae! + Age! (2.44) Case 3, If q <wp the roots are complex and the circuit is said to be uunderdamped. The roots are sa = et ju, (2.45) 2.11 Diodes with LC and ALCLoads 53 where w, is called the ringing frequency (or damped resonant frequency) and q, = Vw ?. The solution takes the form de) = (A cosw, + Assinta,t) (2.46) which is a damped or decaying sinusoidal. Note: The constants A, and A, can be determined from the initial conditions of the circuit. The ratio of a/wg is commenly known as the damping ratio, ô = R2WCIL. Power electronic circuits are generally underdamped such that the circuit current be- comes near sinusoidal, to cause a nearly sinusoidal ac output or to turn off a power semiconductor device. Example 2.6 Finding the Current in an ALC Circuit The second-order RLC circuit of Figure 2.17 has the de source voltage V, = 220 V, inductance L = 2mH, capacitance € = 0.05 gF, and resistance R = 160 8). The initial value of the capaci- tor voltage is (1 = 0) = Vo = 0 and conductor currenti(r = 0) = 0. 1f switch 5, is closed at t = 0, determine (a) an expression for lhe current i(t). and (b) the conduction time of diode, (c) Draw a sketch of i(t). (d) Use PSpice to plot the instantaneous current i for R = 50 0), 160), and 320 1. Solution a. From Eq. (2.40),a = RBL = 160 x 1042 x 2) = 40,000 radis, and from Eq. (2.41), ug = VLC = 10º radis, The ringing frequency becomes o, = 4/10! = 16 x 105 = 91,652 radis Because a < uy, itis an underdamped circuit and the solution is of the form Hr) = eM(Apcosw, + Ajsinw,) Atr= Oi(r=0)=Oandthisgives A, = 0 The solution becomes (rn) = e As sin ut The derivative of i(t) becomes di a . a dt =u, cosw Ae “ = asine, Age When the switch is closed atr = O, capacitor offers a low impedance and the in- ductor offers a high impedance. Th al rate of rise of the current is limited only by the inductor L. Thus at ! = 0, the circuit difdtis V/L. Therefore, E dia which gives the constant as V x 14 «20X 1000 o, GO DAS X2 54 Chapter2 | Power Semiconductor Diodes and Circuits iamp FIGURE 2.18 Current waveform for Example 2.6. The final expression for the current i(t) is i(t) = 12sin(91,652r)e “UMA b. The conduction time 4, of the diode is obtained when é = O. Thatis, Sh=m or n= gre = 3427ps € The sketch for the current waveform is shown in Figure 2.18. d. The circuit for PSpice simulation [4] is shown in Figure 2.19. The list of the circuit file is as follows: Example 2.6 RLC Circuit with Diode -PARAM VALU = 160 ;Define parameter VALU «STEP PARAM VALU LIST 50 160 320 : Vary parameter VALU vs 1 0 PoL (0 O INS 220V I1MS 220V) ; Piecewise linear R 23 (VALU) ; Variable resistance L 3 4 24H c 40 D.05Ur Dl 12 DMOD : Diode with model DMOD «MODEL DMOD D(IS=2,22E-15 EV=1800V) : Diode model parameters «TRAN 0.105 60US ; Transient analysis - PROBE + Graphics postprocessor «END The PSpice plot of the current K(R) through resistance R is shown in Figure 2.20. The cur- rent response depends on the resistance R. With a higher value of R, the current becomes more damped; and with a lower value, it tends more toward sinusoidal. For R = 0, the peak current becomes V(C/L) = 220 x (0.05 u'2m) = 1.56 A. 2.12 Freewheeling Diodes 57 and i> are defined as the instantancous currents for mode 1 and mode 2, respectively, f, and t are the corresponding durations of these modes. Mode 1. During this mode, the diode current i,, which is similar to Eq. (2.25), is Y io) = 001 - ti) (2.47) When the switch is opened at 1 = 1 (at the end of this mode), the current at that time becomes h=i(t=n)= Ea = grRiL) (2.48) JE the time 1y is sufficiently long, the current practically reaches a steady-state current off, = V/R flows through the load. Mode 2. This mode begins when the switch is opened and the load current starts to flow through the freewheeling diode D,,. Redefining the time origin at the be- ginning of this mode, the current through the freewheeling diode is found from di 0= LT + Ri (2.49) with initial condition is(t = 0) = 1,. The solution of Eq. (2.49) gives the freewheeling currentip = dp as ialt) = fe (2.50) and at t = this current decays exponentially to practically zero provided that to => L!R, The waveforms for the currents are shown in Figure 2.21c, Note: Figure 2.21c shows that at t and 4», the currents have reached the steady- state conditions. These are the extreme cases. À circuit normally operates under condi- tions such that the current remains continuous. Example 2.7 Finding the Stored Energy in an Inductor with a Freewheeling Diode In Figure 2.2ta, the resistance is negligible (R = 0), the source voltage is V, = 220 V (constant time), and the load inductance is L = 220 nH. (a) Draw the waveform for the load current if the switch is closed for a time 1, = 100 ps and is then opened. (b) Determine the final energy stored in the load inductor. Solution a. The circuit diagram is shown in Figure 2.22a with a zero initial current, When the switch is closed at! = O, the load current rises lincarly and is expressed as ide) E andatt = n,dy = Vr/L = 220 x 100220 = 100 A. Chapter2 | Power Semiconductor Diodes and Circuits been H (a) Circuit diagram (b) Waveforms FIGURE 2.22 Diode circuit with an L load. b. When switch S, is openedata time! = &,, the load current starts to flow through diode Dm Because there is no dissipative (resistive) element in the circuit, the load current remains constant at ly = 100 A and the energy stored in the inductor is 0.5L/3 = 1,1J. The current waveforms are shown in Figure 2.22b. Key Points of Section 2.12 * If the load is inductive, an antiparallel diode known as the freewheeling diode must be connected across the load to provide a path for the inductive current to flow. Otherwise, energy may be trapped into an inductive load. RECOVERY OF TRAPPED ENERGY WITH A DIODE In the ideal lossless circuit [7] of Figure 2.22a, the energy stored in the inductor is trapped there because no resistance exists in the circuit. In a practical circuit it is desir- able to improve the efficiency by returning the stored energy into the supply source. This can be achieved by adding to the inductor a second winding and connecting à diode D, as shown in Figure 2.23a. The inductor and the secondary winding behave as a transformer. The transformer secondary is connected such that if w is positive, vz is negative with respect to w, and vice versa. The secondary winding that facilitates re- tuming the stored energy to the source via diode D, is known as a feedback winding. Assuming a transformer with a magnetizing inductance of L,,, the equivalent circuit is as shown in Figure 2.23b. If the diode and secondary voltage (source voltage) are referred 10 the primary side of the transformer, the equivalent circuit is as shown in Figure 2.23c. Parameters i and i; define the primary and secondary currents of the transformer, respectively. 213 Recovery of Trapped Energy with a Diode 59 + Vo — q 81 D N i A Do Ny:No + t=0 h + - . v n | fo - * + Ny:N> (a) Circuit diagram S1 ai Ny:N) a 1:Np . Ideal transformer (b) Equivalent circuit (c) Equivalent circuit, referred to primary side FIGURE 2.23 Circuit with an energy recovery diode. [Ref 7,8. Dewan] The turns ratio of an ideal transformer is defined as = (2.51) The circuit operation can be divided into two modes. Mode 1 begins when switch 5, is closed at + = 0 and mode 2 begins when the switch is opened. The equivalent circuits for the modes are shown in Figure 2.24a, with 4, and t, the durations of mode 1 and mode 2, respectively. 62 Chapter 2 Power Semiconductor Diodes and Circuits Example 2.8 Finding the Recovery Energy in an Inductor with a Feedback Diode For the energy recovery circuit of Figure 2.23a, the magnetizing inductance of the transformer is Lm = 250 pH, N, = 10, and M$ = 100. The leakage inductances and resistances of the trans- former are negligible. The source voltage is V, = 220 V and there is no initial current in the cir- cuit. lí switch S, is closed for a time 1 = 50 us and is then opened, (a) determine the reverse voltage of diode D, (b) calculate the peak value of primary current, (c) calculate the peak value of secondary current, (d) determine the conduction time of diode D,, and (e) determine the en- ergy supplied by the source. Solution The tums ratiois a = NyN, = 100/10 = 10. a. From Eq. (2.52) the reverse voltage of the diode, vp =Vil+a)=220X(1+10)=2420V r From Eq. (2.55) the peak value of the primary current, Y so h=Tot=200 x MA The peak value of the secondary current 1g = la = 44/10 = 4.4 A. From Eq. (2.58) the conduction time of the diode pe abalo 10 n= = 250 X 44 X 5 = 50045 1 e. The source energy, H w= [uid- 0 Using h from Eg. (2.55) yields W = 05Lylj =0.5X 250 x 10% x 44? = 0.242] =242m] Key Points of Section 2.13 * The trapped energy of an inductive load can be fed back to the input supply through a diode known as the feedback diode, SUMMARY The characteristics of practical diodes differ from those of ideal diodes. The reverse recovery time plays a significant role, especially at high-speed switching applications. Diodes can be classified into three types: (1) gencral-purpose diodes, (2) fast-recovery diodes, and (3) Schottky diodes. Although a Schottky diode behaves as a pr-junction Review Questions 63 diode, there is no physical junction; and as a result a Schottky diode is a majority car- rier device. Onthe other hand, a pa-junction diode is both a majority and a minority carrier diode. Té diodes are connected in series to increase the blocking voltage capability, voltage-sharing networks under steady-state and transient conditions are required. When diodes are connected in parallel to increase the current-carrying ability, current-sharing elements are also necessary. In this chapter we have seen the applications of power diodes in voltage reversal of a capacitor, charging a capacitor more than the de input voltage, freewheeling ac- tion, and energy recovery from an inductive load. REFERENCES [1] M.H. Rashid, Microelectronic Circuits: Analysis and Design. Boston: PWS Publishing. 1999, Chapter 2. [2] PR Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits New York: John Wiley & Sons. 1993, Chapter 1. [3] Infineon Technologies: Power Semiconductors. Germany: Siemens, 2001, wwwinfineon.com/ [4] M.H. Rashid, SPICE for Circuits and Electronics Using PSpice. Englewood Cliffs, NJ: Prentice-Hall Inc, 1995. [5] M. H. Rashid, SPICE for Power Electronics and Electric Power. Englewood Cliffs, NJ: Prentice-Hall. 1993. [6] P'WTuinenga, SPICE: A guide to Circuit Simulation and Analysis Using PSpice. Engle- wood Clifís, NJ: Prentice-Hall. 1995. [7] S.B. Dewan and A. Straughen, Power Semiconducior Circuits. New York: John Wiley & Sons. 1975, Chapter 2. REVIEW QUESTIONS 2.1 Whalare the types of power diodes? What is a leakage current of diodes? What is a reverse recovery time of diodes? What is a reverse recovery current of diodes? What is a softness factor of diodes? NWhat are the recovery types of diodes? What às the cause of reverse recovery time in a pr-junction diode? What is the effect of reverse recovery time? 29 Why is il necessary to use fast-recovery diodes for high-speed switching? 2.10 What is a forward recovery time? 2.11 What arc the main differences between pr-junction diodes and Schotiky diodes? 2.12 What are the limitations of Schotiky diodes? 213 What is the typical reverse recovery time of general-purpose diodes? 2.14 What is the typical reverse recovery time of fast-recovery diodes? 215 Whal are the problems of series-connected diodes, and what are the possible solutions? 2.16 What are the problems of parallel-connected diodes, and what are the possible solutions? 217 If two diodes are connected in series with equal-voltage sharings, why do the diode leak- age currents diffcr? BRERELE 64 Chapter? Power Semiconductor Diodes and Circuits 218 219 20 221 BRE E PROBLEMS 2 22 What is the time constant ofan RL circuit? What is the time constant of an RC circuit? What is the resonant frequency of an LC circuit? What is the damping factor of an RLC circuit? What is the difference between the resonant frequency and the ringing frequency of an RLC circuit? What is a freewheeling diade, and what is its purpose? What is the trapped energy of an inductor? How is the trapped energy recovered by a diode? The reverse recovery time of a diode is f, = 5 us, and the rate of fall of the diode current is difdt = 80 Als. 1 the softness factor is SF = 0.5, determine (a) the storage charge Qar and (b) the peak reverse current fap. The measured values of a diode at a temperature of 25 “C are Vo=10Vatip=50A =15Vatip= 6004 Determine (a) the emission coefficient n, and (b) the leakage current 1, Two diodes are connected in series and the voltage across each diode is maintained the same by connecting a voltage-sharing resistor, such that Vp = Vpz =2000V and Ry = 100k1). The v-i characteristics of the diodes are shown in Figure P2.3. Determine the leakage currents of each diode and the resistance R; across diode Ds. + I 1 1 1 1 FIGURE PZ.3 Problems 67 214 For the energy recovery circuit of Figure 2.23a, the magnetizing inductance of the trans- 215 former is Lm = 150 4H, N, = 10, and N; = 200, The leakage inductances and resis- tances of the transformer are negligible. The source voltage is V, = 200 V and there is no initial current in the circuit. If switch 5, is closed for a time 1, = 100 ps and is then opened, (a) determine the reverse voltage of diode Dy, (b) calculate the peak primary current, (ce) calculate the peak secondary current, (d) determine the time for which diode D, conducts, and (e) determine the energy supplied by the source. A diode circuit is shown in Figure P2.15 where the load current is flowing through diode D,. If switch 5, is closed at a lime + = 0, determine (a) expressions for v,(t), it). and ia(r); (b) time 1, when the diode D, stops conducting; (e) time 1, when the voltage across the capacitor becomes zero; and (d) the time required for capacitor to recharge to the sup- ply voltage 4. 5 |» FIGURE P2,15 CHAPTER 3 Diode Rectifiers The leaming objectives of this chapter are as follows: ...... 3.1 32 To understand the operation and characteristics of diode rectifiers To leam the types of diode rectifiers To understand the performance parameters of diode rectifiers To leam the techniques for analyzing and design of diode rectifier circuits To leam the techniques for simulating diode rectifiers by using SPICE To study the effects of load inductance on the load current INTRODUCTION Diodes are extensively used in rectifiers. À rectifier is a circuit that converts an ac sig- nal into a unidirectional signal. A rectifier is a type of dc-ac converter. Depending on the type ofinput supply, the rectifiers are classified into two types: (1) single phase and (2) three phase. For the sake of simplicity the diodes are considered to be ideal. By “ideal” we mean that the reverse recovery time t,, and the forward voltage drop Vp are negligible. That is, t,, = O and Vo = O. SINGLE-PHASE HALF-IWWAVE RECTIFIERS A single-phase half-wave rectifier is the simplest type, but it is not normally used in in- dustrial applications. However, it is useful in understanding the principle of rectifier operation. The circuit diagram with a resistive load is shown in Figure 3.1a. During the positive half-cycle of the input voltage, diode D, conducts and the input voltage ap- pears across the load. During the negative halí-cycle of the input voltage, the diode is in a blocking condition and the output voltage is zero. The waveforms for the input volt- age and output voltage are shown in Figure 3.1b, Key Points of Section 3.2 * The half-wave rectifier is the simplest power electronics circuit that is used for low-cost power supplies for electronics like radios. 3.3 Performance Parameters 69 aja -----a (a) Circuit diagram (b) Waveforms. FIGURE 3.1 Single-phase half-wave rectificr. PERFORMANCE PARAMETERS Although the output voltage as shown in Figure 3.1b is de, it is discontinuous and con- tains harmonics. À rectifier is a power processor that should give a de output voltage with a minimum amount of harmonic contents. At the same time, it should maintain the input current as sinusoidal as possible and in phase with the input voltage so that the power factor is near unity. The power-processing quality of a rectifier requires the determination of harmonic contents of the inpul current, the output voltage, and the output current. We can use Fourier series expansions to find the harmonic contents of voltages and currents. There are different types of rectifier circuits and the perfor- mances of a rectifier are normally evaluated in terms of the following parameters: The average value of the output (load) voltage, Vá. The average value of the output (load) current, Ay The output de power, Fã = Vaclg (3.1) The root-mean-square (rms) value of the output voltage, Vim The rms value of the output current, Arms The output ac power Pa = Vemslons (3.2) 72 Chapter3 Diode Rectifiers However, the frequency of the source is f = 1/T and w = 2nf. Thus Vi Vic = E = 0318Vy 2 Vie 0318M, lu="p R (3.13) The rms value of a periodic waveform is defined as ter [Hf ima] For a sinusoidal voltage of w(t) = Va Sin ot for 0 = 1 = T/2, the rms value of the output voltage is Ta 12 =ll in ur? = ms Vim = E) (Va Sin ur) di] =5 = 054, Im = Vis = Ulm 3.14 mo RR as) From Eg.(3.1), Pa = (0318V,,)JY/R, and from Eq. (3.2), Pe = (054) UR. From Eq. (3.3), the efficiency 9 = (0.318V,, I(0.5V,,)? = 40.5%. From Eq. (3.5), the FF = 0.54,/0.318V,, = 1.57 or 157%. From Eq.(3.7) the RF = 1.57 — 1 = 1.21 or 121%. The rms voltage of the transformer secondary is porre 1 T > IR Va v= T (Umsinwn)Pdt | = 5 = 0707Vg (3.15) The rms value of the transformer secondary current is the same as that of the load: 2 05Vy k R The volt-anpere rating (VA) of the transformer, VA = Vil, = 07074, X 0.5V/R. From Eq. (3.8) TUF = P(V1,) = 0.318%/(0.707 x 0.5) = 0.286. e. The peak reverse (or inverse) blocking voltage PIV = Vr L (ape = Va/R and 4, = 0.5V,/R. The CF of the input current is CF = trem ll; = VOS = 2. & The input PE for a resistive load can be found from 05” Pr PF va TOS = 0,707 Note: 1/TUF = 1/0.286 = 3.496 signifies that the transformer must be 3.496 times larger than that when it is used to deliver power from a pure ac voltage. This rec- tifier has a high ripple factor, 121%; a low efficiency, 40.5%; and a poor TUF, 0.286. In addition, the transformer has to carry a de current, and this results in a de saturation problem of the transformer core. 3.3 Performance Parameters 73 (e) Waveforms FIGURE 3.3 Half-wave rectifier with RL load. Let us consider the circuit of Figure 3.1a with an RL load as shown in Figure 3.3a. Due to inductive load, the conduction period of diode D, will extend beyond 180º until the current becomes zero ate! = 1 + o. The waveforms for the current and voltage are shown in Figure 3.3b. It should be noted that the average v, of the inductor is zero. The average output voltage is v -E[”s ut d! ) = de Jp" = 50) Sina! d(ut) = se f-cos wi] Hm = e [1 - cos(m + o)] (3.16) The average load current is le = VadR. 74 Chapter3 | Diode Rectifiers Tt can be noted from Eq. (3.16) that the average voltage (and current) can be in- ercased by making o = 0, which is possible by adding a freewhecling diode D,, as shown in Figure 3.3a with dashed lines. The effect of this diode is to prevent a negative voltage appearing across the load; and as a result, the magnetic stored energy is in- creased. Att = 4 = m/w, the current from Dy is transferred to D,, and this process is called commutation of diodes and the waveforms are shown in Figure 3.3c. Depending on the load time constant, the load current may be discontinuous. Load current ip is dis- continuous with a resistive load and continuous with a very high inductive load. The continuity of the load current depends on its time constant r = wL/R, Ifthe output is connected to a battery, the rectifier can be used as a battery charger. This is shown in Figure 3.da. For v, > E, diode D, conducts. The angle « when the diode starts conducting can be found from the condition Vasina = E nit R D, AA Pt— + + ta Te OZ ss Pra vt q m (a) Circuit US Um Sin ul FIGURE 3.4 (b) Wavelorms Battery charger. 34 34 Single-Phase Full-wave Rectifiers 77 Key Points of Section 3.3 » The performance of a half-wave rectifier that is measured by certain parameters is poor. The load current can be made continuous by adding an inductor and a freewheeling diode. The output voltage is discontinuous and contains harmonics at multiples of the supply frequency. SINGLE-PHASE FULL-WAVE RECTIFIERS A full-wave rectifier circuit with a center-tapped transformer is shown in Figure 3.5a. Each half of the transformer with its associated diode acts as a half-wave rectifier and the output of a full-wave rectifier is shown in Figure 3.5b. Because there is no de cur- rent flowing through the transformer, there is no dc saturation problem of transformer core. The average output voltage is 2 [TR V, Me 7) Vasinurde = a = 0.6366H, (321) Instead of using a center-tapped transformer, we could use four diodes, as shown in Figure 3,6a. During the positive half-cycle of the input voltage, the power is supplied Vm [+ vos —| (a) Circuit diagram (b) Waveforms FIGURE 3.5 Full.wave rectifier with center-tapped transformer. 78 Chapter3 Diode Rectifiers + % JE» — R$ o, AT 4 a Ypy Vu “or tnr (a) Circuit diagram (b) Waveforms 8 P p FIGURE 3.6 Full-wave bridge rectifier. to the load through diodes D, and Dy. During the negative cycle, diodes D, and D, con- duct. The waveform for the output voltage is shown in Figure 3.6b and is similar to that of Figure 3.5b. The peak-inverse voltage of a diode is only V,,. This circuit is known as a bridge rectifier, and it is commonly used in industrial applications [1,2]. Example 3.4 Finding the Performance Parameters of a Full-Wave Rectifier with Center-Tapped Transformer Ifthe rectifier in Figure 3.5a has a purely resistive load of R, determine (a) the efficiency, (b) the FE (c) the RF, (d) the TUF, (e) the PIV of diode Dy, and (f) the CF of the input current. Solution From Eq. (3.21), the average output voltage is 2, Vi = = = 0.6366V,, and the average load current is Vo D6366V, MR OR 34 Single-Phase Full-Wave Rectifiers 79 The rms value of the output voltage is Ta V Vim = [2 (Ea sin or)? a] = a — 0707V, Vos 0707 ms = R R From Eq. (3.1) Pp. = (0.6366V,,) YR, and from Eq. (32) Pe = (0.707V, IR. a From Eq. (33), the efficiency n = (0.63664,)M(0.707V,,)? = 81%. b. From Eq. (2.5), the form factor FF = 0.7074,/0.6366V,, = 1.11. e From Eg.(3.7), the ripple factor RE = W/LII — 1 = 0,482 0r 482%. d. The rms voltage of the transformer secondary V, = Va/V2 = 0,707V,. The rms value of transformer secondary current 4, = 0.5V,/R. The volt-ampere rating (VA) of the transformer, VA = 2444, = 2 X 0.707V X 0,5V,/R. From Eq. (3.8), 0.6366º TUE = gm x os” 05732 = 5732% e, The peak reverse blocking voltage, PIV = 24. Lo Asp) = Vy/R and 1, = 0.7074,/R. The CF of the input current is CF = Lypeat)/l; = 0.707 = V2 £- The input PF for a resistive load can be found from Pre 0.707 =vaT2x0307x05 077 Note: WYTUF = 1/0.5732 = 1.75 signifies that the input transformer, if present, must be 1.75 times larger than that when it is used to deliver power from a pure ac sinusoidal voltage. The rectifier has an RF of 48.2% and a rectification efficiency of 81%. Note: The performance of a full-wave rectifier is significantly improved compared with that of a half-wave rectifier. Example 3.5 Finding the Fourier Series of the Output Voltage for a Full-Wave Rectifier The rectifier in Figure 3.5a has an RZ load. Use the method of Fourier series to obtain expres- sions for output voltage w(*). Solution The rectifier output voltage may be described by a Fourier series (which is reviewed in Appen dix Ejas o vol) = Vac + A (an cos nor + by Sin nor)